Addendum to "Impact of polarization observables and $B_c\to \tau \nu$ on new physics explanations of the $b\to c\tau \nu$ anomaly"

Abstract

In this addendum to arXiv:1811.09603 we update our results including the recent measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ by the Belle collaboration: $\mathcal{R}(D{)}_{\mathrm{Belle}}=0.307\pm 0.037\pm 0.016$ and $\mathcal{R}(D^{\ast }{)}_{\mathrm{Belle}}=0.283\pm 0.018\pm 0.014$, resulting in the new HFLAV fit result $\mathcal{R}(D)=0.340\pm 0.027\pm 0.013$, $\mathcal{R}(D^{\ast })=0.295\pm 0.011\pm 0.008$, exhibiting a $3.1\sigma$ tension with the Standard Model. We present the new fit results and update all figures, including the relevant new collider constraints. The updated prediction for $\mathcal{R}({\Lambda }_c)$ from our sum rule reads $\mathcal{R}({\Lambda }_c)={\mathcal{R}}_{\mathrm{SM}}({\Lambda }_c)\left(1.15\pm 0.04\right)=0.38\pm 0.01\pm 0.01$. We also comment on theoretical predictions for the fragmentation function $f_c$ of $b\to B_c$ and their implication on the constraint from $B_{u/c}\to \tau \nu$ data.

9 pages, 7 figures. v2: references added, matches PRD version